Chapter 14: Simultaneous Equations1.2.3.4. UE, 14.3.1)5.6.7.The naïve Keynesian macroeconomic model of the U.S. economy identified in UE, p. 477 will be used to demonstrate the two stage-least squares procedure. The data for this model is found in the EViews workfile named macro14.wf1 and it is printed in UE, Table 14.1, p. 478. Twovariables that are included in the macroeconomic model must be generated from other data series (see note at the bottom of UE, Table 14.1, p. 478).Generating time series for taxes and net exports using structural equations (UE, p. 477): Follow these steps to generate time series values for T (taxes) and NX (net exports) using the structural equations in the model:Step 1. Open the EViews workfile named Macro14.wf1.Step 2. To generate a new series named T for taxes, select Genr on the workfile menu bar, type T=Y-YD in the Enter equation: window, and click OK. A new series icon for T is created in theworkfile window.Step 3. To generate a new series named NX for net exports, select Genr on the workfile menu bar, type NX=Y-CO-I-G in the Enter equation: window, and click OK. A new series icon for NX is created in the workfile window.Step 4. Select Save on the workfile menu bar to save your changes.Estimating CO with least squares (UE, Equation 14.31, p. 481):Step 1. Open the EViews workfile named Macro14.wf1.Step 2. Select Objects/NewObject/Equation on the workfilemenu bar, enter CO C YD CO(-1)in the Equation Specification:window, and click OK to revealthe regression output to the right.Step 3. Select Name on the equationwindow menu bar, enter OLS_COin the Name to identify object:window, and click OK.Step 4. Select Save on the workfilemenu bar to save your changes.Estimating two-stage least squares regression using EViews TSLS method (UE, 14.3.1): To estimate the two-stage least squaresmodel printed in UE, Equation 14.29,follow these steps:Step 1. Open the EViews workfile namedMacro14.wf1.Step 2. Select Objects/NewObject/Equation on the workfilemenu bar, and select TSLS – Two-StageLeast Squares (TSNLS and ARMA) inthe Method: window under EstimationSettings: and the dialog will change toinclude an Instrument list: window (seegraphic on the right).Step 3. Enter CO C YD CO(-1) in theEquation Specification: window and C G T NX CO(-1) R(-1) in the Instrument list: window.1 The graphic above shows the relevant selections/entries highlighted in yellow. Click OK to reveal the Estimation Output view printed below. The yellow highlighted portions of theregression output reflect the selections made in the dialog window shown above.2Dependent Variable: COMethod: Two-Stage Least SquaresDate: 07/10/00 Time: 15:12Sample(adjusted): 1964 1994Included observations: 31 after adjusting endpointsInstrument list: C G T NX CO(-1) R(-1)t-StatisticErrorProb.Std.Variable CoefficientC -24.73014 34.90233 -0.708553 0.4845YD 0.441638 0.153839 2.870773 0.0077CO(-1) 0.540309 0.163000 3.314782 0.0025R-squared 0.997890 Mean dependent var 2445.210Adjusted R-squared 0.997739 S.D. dependent var 642.2594S.E. of regression 30.53734 Sum squared resid 26110.82F-statistic 6615.725 Durbin-Watson stat 0.982576Prob(F-statistic) 0.000000Step 4. Select Name on the equation window menu bar, enter TSLS_CO in the Name to identify object: window, and click OK.Step 5. Select Save on the workfile menu bar to save your changes.1 The constant, C, is always a suitable instrument, so EViews will add it to the instrument list if you omit it.2 EViews identifies the estimation procedure, as well as the list of instruments in the header. This information isfollowed by the usual coefficient, t-statistics, and asymptotic p-values. EViews uses the structural residuals in calculating all of the summary statistics. These structural residuals should be distinguished from the second-stage residuals that you would obtain from the second-stage regression if you actually computed the two-stage least squares estimates in two separate stages.Estimating two-stage least squares regression using two distinct stages and OLS (UE, 14.3.1): To estimate the two-stage least squares equation printed in UE, Equation 14.28, using ordinary OLS and two distinct phases, follow these steps:Step 1. Open the EViews workfile named Macro14.wf1.Step 2. To estimate the reduced form equation for YD (UE, Equation 14.27, p. 480), select Objects/New Object/Equation on the workfile menu bar, enter YD C G NX T CO(-1) R(-1) in the Equation Specification: window, and click OK.Step 3. To generate the forecast values from this equation, select Forecast on the equation menu bar, enter YDF in the Forecast name: window, and click OK. EViews will create a new variable in the workfile named YDF.Step 4. To estimate the second stage equation for CO (UE, Equation 14.29, p. 481), select Objects/New Object/Equation on the workfile menu bar, enter CO C YDF CO(-1) in theEquation Specification: window, and click OK. Note that we have used the instrumental variable YDF instead of the actual variable YD for disposable income. The method, dependent variable, and variable names are highlighted in yellow in the OLS regression output shown below.Step 5. Select Name on the equation window menu bar, enter TSLS_OLS_CO in the Name to identify object: window, and. click OK.Step 6. Select Save on the workfile menu bar to save your changes.Dependent Variable: COMethod: Least SquaresDate: 07/05/00 Time: 15:44Sample(adjusted): 1964 1994Included observations: 31 after adjusting endpointst-StatisticErrorProb.Variable CoefficientStd.C -24.73014 41.09577 -0.601769 0.5522YDF 0.441638 0.181138 2.438126 0.0214CO(-1) 0.540309 0.191924 2.815219 0.0088R-squared 0.997075 Mean dependent var 2445.210Adjusted R-squared 0.996866 S.D. dependent var 642.2594S.E. of regression 35.95622 Akaike info criterion 10.09425Sum squared resid 36199.78 Schwarz criterion 10.23302Log likelihood -153.4608 F-statistic 4771.906Durbin-Watson stat 1.485932 Prob(F-statistic) 0.000000Comparing the OLS, EViews TSLS, and OLS two-stage models:To compare the coefficients, std. Errors, and t-statistics for the three models discussed in this chapter, open the equations named OLS_CO, TSLS_CO and TSLS_OLS_CO, by double clickingfor each regression.Note that the estimated coefficients are larger in the OLS_CO model compared to the TSLS_CO and TSLS_OLS_CO models. This supports the hypothesis that OLS estimates of coefficients have a positive bias in simultaneous equation models (simultaneity bias). Contrarily, TSLS estimated coefficients tend to have a downward bias. Note that the estimated coefficients are identical for the TSLS_CO and TSLS_OLS_CO models, but the standard errors (Std. Error in the EViews output) are smaller in the EViews TSLS estimated model, making the coefficients more significant (i.e., higher t-statistics). In order to get accurate estimates of standard errors and t-scores, the estimation should be done on a complete two-stage least squares program (like EViews TSLS). When OLS is used to estimate the second stage, it ignores the fact that the first stage was run at all (UE, footnote 11, p. 481).The identification problem and the order condition (UE, 14.3.3):In order to calculate two-stage least squares using the TSLS – Two-Stage Least Squares (TSNLS and ARMA) option, your specification must satisfy the order condition for identification, which states that there must be at least as many instruments as there are coefficients in your equation.The order condition for identification is easy to assess in EViews. Count, to make sure that the number of independent variables, not counting the constant, in the Equation Specification: window (i.e., YD & CO(-1)Exercises:9.12. Double click the icon in the EViews Macro14.wf1 workfile window to re-activate the UE, Equation 14.29. Click Estimate on the equation menu bar and click OK.The reason for this is to make sure that the residuals in the EViews workfile are from the TSLS_CO equation. If theb.13. Open EViews and open the EViews workfile named Oats14.wf1.a.b.。
